Figure 3.
Combined wit h th e fac t tha t ^
q
i s a non-negativ e function , th e latte r
shows that th e integra l i n formula (1.2) is minimal whe n al l the coordinate s
of the vecto r £ are equal , an d i t i s maximal whe n on e o f the coordinate s i s
equal t o 1 and th e other s ar e equa l t o zero .
D
Figure 4 . £^-ball s
To conclude thi s sectio n le t u s give an overvie w o f known result s o n th e
extremal section s o f £™-balls.
q o o
max: £ = ( ^ , ^ , 0 , . . . ,0) , Ball [Bai ]
min: £ = (1,0, ...,0), Hadwige r [Ha] , Hensle y [He] , Vaale r
[V]
0 q 2
max: £ = (1,0,..., 0), Meyer-Pajor [MeyP ] ( 1 q 2),
Caetano [C] , Barthe [Bar ] ( 0 q 1).
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